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Algebraic characterization of the isometries of the hyperbolic 5-space. (English) Zbl 1190.37022
The author obtains an algebraic characterization of the dynamical types of the orientation preserving isometries of the hyperbolic 5-space 5 . The characterization is described by using the representation of the isometries of 5 as 2×2 matrices over the quaternions, 𝔾𝕃(2,), together with the natural embedding of 𝔾𝕃(2,) into 𝔾𝕃(4,). It is also given the determination of the conjugacy classes and the z-classes in 𝔾𝕃(2,).
MSC:
37C85Dynamics of group actions other than and , and foliations
51M10Hyperbolic and elliptic geometries (general) and generalizations
15A33Matrices over special rings
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